K-extreme point of generalized Orlicz sequence spaces with Luxemburg norm

• Autorzy: Shi Z. , Wang X.

Identyfikatory

DOI

10.14708/cm.v53i2.790

• Języki publikacji: EN

Abstrakty

EN

In this paper,we give necessary and sufficient conditions in order that a point u∈S(l_(Φ)) is a k-extreme point in generalized Orlicz sequence spaces equipped with the Luxemburg norm, combing the methods used in classical Orlicz spaces and new methods introduced especially for generalized ones. The results indicate the difference between the classical Orlicz spaces and generalized Orlicz spaces.

Słowa kluczowe

EN

Orlicz function; k-extreme point; linear dependence; Luxemburg norm

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: Vol. 53, No. 2
• Strony: 147--162
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Shi Z.

• Department of Mathematics, Shanghai University, Shanghai 200444, P.R.China

autor

Wang X.

• Department of Mathematics, Shanghai University, Shanghai 200444, P.R.China

Bibliografia

• [1] Mihai M and Vicentiu R. Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: An Orlicz-Sobolev space setting. J. Math. Anal. Appl, 330 (2007), 416-432.
• [2] Birnbaum Z W and Orlicz W. Über die Verallgemeinerung des Begriffes der zueinander Konjugierten Potenzen. J. Studia Mathematica, 3 (1931), 1-67.
• [3] Biang S and Frittelli M. A unified framework for utility maximiztion prblems: an Orlicz space approach. J. The Annals of Applied Probability, 18(3) (2008), 929-966.
• [4] Singer I. On the set of best approximation of an element in normed linearly space. J. Rev. Roum. Math. Pree. Appl, 5 (1960), 23-35.
• [5] Sullivan F. A generalization of uniformly rotund Banach spaces, Canad, J. Math, 31 (1979), 628-636.
• [6] Nan C X and Wang J H. K-rotundity and K-smoothy. Chinese Annals of Mathematics, 3 (1990), 321-324.
• [7] Carath´eodory C. Über den Variabilitätsbereich der Fourier’schen Konstanten von positive harmonischen Funktionen. Rend. Circ. Mat. Palermo, 32 (1911), 193-217.
• [8] Zhong T Y, Zhang Y F and Cui Y A. k-rotundity and k-smooth in Orlicz sequence spaces. Journal of Harbin Engineering University, 19 (1998), 93–98.
• [9] Chen S T. Geometry of Orlicz spaces, Dissertationes Mathematicae, 356 (1996), 1-204.
• [10] Hudzik H and Pallaschke D. On some Convexity properties of Orlicz sequence spaces Equipped with the Luxemburg Norm, J. Math. Nachr, 186 (1997), 167-185.
• [11] Wang Z Q. Extreme point in Orlicz sequence spaces, Journal of Daqing petroleum institute, 17 (1983), 112-121.